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CA Foundation · Quantitative Aptitude · Equations

For which value of k does the equation x² − (k + 2)x + 9 = 0 have roots that are equal in magnitude but opposite in sign? Choose the correct statement about k and the roots.

The value is k = −2, but then the equation becomes x² + 9 = 0, which has no real roots. Opposite roots need a zero sum, so k + 2 = 0. Real roots of 3 and −3 would require a constant term of −9, not 9.

  1. Ak = −2, but the roots are then not realCorrect
  2. Bk = 2, roots are 3 and −3
  3. Ck = 4, roots are 3 and −3
  4. Dk = −2, roots are 3 and −3

Explanation

Roots equal and opposite need sum zero, so k + 2 = 0, giving k = −2. The equation becomes x² + 9 = 0, so x² = −9, which has no real roots. Hence the other options claiming roots 3 and −3 are wrong, since that would need the constant term to be −9.

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